Spin resonance spectroscopy (ESR) or Electron paramagnetic resonance (EPR) is a widely used technique for studying and characterizing materials with unpaired electrons. The technique depends on the fact that certain atomic systems have a permanent magnetic moment. The energy levels of the magnetic system are influenced by the surrounding atoms and by external magnetic fields.
Every electron has a magnetic moment and spin quantum number s=½, with magnetic components ms=+½ and ms=−½. In the presence of an external magnetic field with strength B0, the electron's magnetic moment aligns itself either parallel or antiparallel (ms=−½ or ms=+½ respectively) to the field, each alignment having a specific energy due to the Zeeman effect. Therefore, the splitting of the energy levels between the lower and the upper state of energy ΔE is directly proportional to the magnetic field's strength. An unpaired electron can move between the two energy levels by either absorbing or emitting a photon of energy hν such that the resonance condition, hν=ΔE, is obeyed. This leads to the fundamental equation of ESR (or EPR) spectroscopy: hν=ge*μB*B0, where ge is the electron's so-called g-factor, μB is the Bohr magneton and B0 is the external magnetic field applied to the material.
Once the energy levels of a system have been found, one needs to find an appropriate manner to detect them.
A first detection approach is the consideration of the absorption of electromagnetic radiation due to transitions between levels. This absorption will occur when hν=ΔE. In the case of magnetic phenomena, energy absorption occurs in response to an alternating magnetic field of the radiation. Generally, a main external magnetic field B0 is produced by an electromagnet, controlled by a power supply controller which allows the magnetic field to be ramped slowly up or down. A microwave generator and resonant cavity are used to provide a time-varying magnetic field H. A lock-in amplifier is used to detect the reduction in microwave power produced by the ESR/EPR absorption. In addition, the required alternating magnetic field H is generally produced by a solid state oscillator operating in general in the GHz range. The oscillator is coupled to the resonant cavity containing the sample which is exposed to microwaves at a fixed frequency. By increasing the external magnetic field B0, the gap between the ms=+½ and ms=−½ energy states is widened until it matches the energy of the microwaves. At this point the unpaired electrons can move between their two spin states. Since there are typically more electrons in the lower state, due to the Maxwell-Boltzmann distribution, there is a net absorption of energy, and it is this absorption that is monitored and converted into a spectrum. When the oscillator frequency matches the cavity frequency, the amplitude of the magnetic field H is increased relative to the oscillator amplitude by the Q-factor of the cavity. Since Q is in the range of a few thousands, this substantially enhances the field intensity and hence the absorption by the sample. Some of the power entering the cavity is allowed to leak out the opposite side. The amount of leakage is determined by the input power and by sample absorption. The output power falls on a diode which converts it to a near-DC. This voltage, proportional to the transmission through the cavity, constitutes the output signal.
A second detection approach is the use of the basic concept which is analogous of nuclear magnetic resonance (NMR), but it is electron spins that are excited instead of the spins of atomic nuclei. The principle of this detection method involves two sequential steps:
i) the alignment (or polarization) of the spins in an applied and constant magnetic field B0, and
ii) the perturbation of this alignment of the spins by employing an electro-magnetic signal H varying with time (usually in radio frequency range).
As shown in the ESR equation above, the required perturbing frequency of H is dependent upon the static magnetic field B0 and the spins of the material of observation. Theoretically, the two fields are to be perpendicular to each other to maximize the ESR signal strength. Resonant absorption by spins will occur only when electromagnetic radiation of the correct frequency (e.g., equaling the Larmor precession rate) is being applied to match the energy difference between the spin levels in a constant magnetic field B0 of the appropriate strength.
Recently, proposals regarding the exploitation of ESR property of endohedral fullerenes in a solid state atomic clock have been made. Such atomic clocks plan to combine the sharp resonance of ESR of endohedral fullerenes and their small size to create high stability frequency and time-keeping standards thanks to the sharp linewidth of the split of the energy levels of the material used.
For example, such atomic clock using endohedral fullerenes is described in document U.S. Pat. No. 7,142,066. However, the alignment device described in this document is not optimal since it creates spatial variations of the value and of the direction of the magnetic field B0 over the spatial range of the solid layer, due notably to the so-called “corner effects” of the magnetic field generated by the alignment device. In other words, the corner effects induced a non-homogenous magnetic field in the spatial range of the solid stated used. As the above equation of ESR shows, the excitation frequency at which ESR/EPR occurs exhibits a strong dependency towards the value of the applied external magnetic field B0. Thus, such gradient of the magnetic field value creates larger absorption spectra of the particles and therefore an output clock signal that exhibits an increased linewidth.
In addition, in this document U.S. Pat. No. 7,142,066, the excitation is created within the plane of the substrate by a varying magnetic field H generated by two capacitors. As mentioned earlier, maximum signal at resonance occurs when excitation magnetic field H is orthogonal to the fixed magnetic field B. Hence the variation of the direction of the magnetic field would translate into a lower useful signal as only the particles having their spin perpendicular to the field generated by the excitation device would contribute to the output signal.
Moreover, in this document U.S. Pat. No. 7,142,066, the sensitivity of the device to external fields (like any electro-magnetic field present in a mobile handset), which can also strongly affect the device performance, is not addressed. Practical manufacturing of the device described in this document is also not optimized. The ability to deposit magnetic material on top of a semiconductor wafers (or die) is limited by the thermal budget of the underlying electronics and materials. Typical sputtering of magnetic material requires high temperature (between 500° C. and 650° C.) processing to obtain magnetic properties practically useful. At such temperatures, the underlying electronics and transistors are affected.
In order to alleviate some of the above identified problems, document U.S. Pat. No. 8,217,724 recommends a device in which the medium must be a specific material for which two particular energy levels have an energy difference that is, to first order, independent of the magnetic field intensity over a certain range.
In addition, it recommends the use of micro-coils as a magnetic device to apply an adjustable magnetic field to the medium. However, in order to generate the required biasing field B0, some current needs to flow constantly in the micro-coils during the device operation which makes this solution incompatible with most recent mobile handsets power consumption requirements.
Moreover, the excitation is performed using a microwave and output signal is then generated using a feedback control loop based on the detection of absorption of the exciting electro-magnetic wave. However, the energy level of the transition requires excitation at a few tens of Mega Hertz which requires resonant cavities and waveguides in the millimeter range. Such dimensions are completely incompatible with miniaturization and costs requirements, notably in the industry of mobile handsets and Internet of Things (IOT).
Another drawback of the solution described in this document is the complexity of operating the device and the number of elements which need to be combined to operate. As an example, operating the device starts with locking the magnetic field to a certain value using a field stabilization circuit and feedback loop system based on absorption of electromagnetic wave. Such operation typically requires unnecessary complexity in the electronics circuitry.